Research Article: Financial time series forecasting using twin support vector regression

Date Published: March 13, 2019

Publisher: Public Library of Science

Author(s): Deepak Gupta, Mahardhika Pratama, Zhenyuan Ma, Jun Li, Mukesh Prasad, Francisco Martínez-Álvarez.

http://doi.org/10.1371/journal.pone.0211402

Abstract

Financial time series forecasting is a crucial measure for improving and making more robust financial decisions throughout the world. Noisy data and non-stationarity information are the two key factors in financial time series prediction. This paper proposes twin support vector regression for financial time series prediction to deal with noisy data and nonstationary information. Various interesting financial time series datasets across a wide range of industries, such as information technology, the stock market, the banking sector, and the oil and petroleum sector, are used for numerical experiments. Further, to test the accuracy of the prediction of the time series, the root mean squared error and the standard deviation are computed, which clearly indicate the usefulness and applicability of the proposed method. The twin support vector regression is computationally faster than other standard support vector regression on the given 44 datasets.

Partial Text

For the last two decades in the machine learning area, support vector machines (SVMs) have been a computationally powerful kernel-based tool for various classification problems, such as pattern recognition and regression problems and function approximations [1]. It has the advantages over other methods, such as artificial neural networks (ANN), which focus on minimizing the empirical risk in the training phase, whereas SVM was developed on the structural risk minimization principle [1], which minimizes the upper bound on the generalization error. Another advantage of SVM is that it forms a convex optimization problem, a single large quadratic programming problem (QPP) that yields a unique global solution. The SVM has been applied in many fields to solve various well-known real-world problems ranging from image classification [2], remote sensing image classification [3], text characterization [4], biomedicine [5, 6], time series prediction [7, 8] and business prediction [9], which clearly justify its popularity.

This section describes the standard formulation of support vector regression (SVR). Assume that a set of training samples is {(x1,y1)}i = 1,2,…,m where xi = (xi1,xi2,…,xin)t∈Rn is the input example and yi∈R is the target value for i = 1,2,…,m, where m corresponds to input training samples. Let matrix D∈Rm×n denote the input examples where xit is the i-th row and y = (y1,…,ym)t is the vector of observed values. The main goal of SVR is to approximate the regression function f(.) in the form
f(x)=xtw+b(1)
where unknowns w is the vector and b is a scalar value.

To further improve the generalization performance and training time of SVR, a new approach was discussed by Peng [20], termed TSVR. The TSVR constructs a pair of nonparallel hyperplanes such that one of the hyperplanes determines the ε-insensitive downbound f1(x) = xtw1+b1 and another ε-insensitive upbound function f2(x) = xtw2+b2 to identify the end regression function. The TSVR solves a pair of smaller QPPs of m constraints to identify the solution instead of solving a single large QPP with a 2 m number of constraints.

In this section, various numerical experiments are conducted to test the generalization performance and the computational efficiency of the TSVR on standard datasets and compared with SVR. This paper considered 44 benchmark datasets and divided them into two groups. The first group has a combination of 24 individual company stocks, and the second group has 20 stock market index datasets from the Yahoo financial website, i.e., http://finance.yahoo.com [38]. Individual company stock datasets are AT&T Inc. (T), Infosys Limited (INFY), Apple, Inc. (AAPL), Facebook, Inc. (FB), Cisco Systems, Inc. (CSCO), Alphabet, Inc. (Goog), Citigroup, Inc. (C), HSBC Holding Plc (HSBC), ICICI Bank, Ltd. (IBN), Royal Bank of Canada (RY), Royal Bank of Scotland (RBS), State Bank of India (SBIN.NS), Punjab National Bank (PNB.NS), International Business Machines Corporation (IBM), Microsoft Corporation (MSFT), Tata Consultancy Services Limited (TCS.BO), Oracle Corporation (ORCL), Bharat Petroleum Corporation Limited (BPCL.NS), Oil India Limited (OIL.NS), Oil and Natural Gas Corporation (ONGC.NS), Royal Dutch Shell Plc (RDS-B), Exxon Mobil Corporation (XOM), Sinopec Shanghai Petrochemical Company Limited (SHI), Hindustan Petroleum Corporation Limited (HINDPETRO.NS) and the stock market index datasets are S&P BSE SENSEX (BSESN), NIFTY 50 (NSEI), CAC 40 (FCHI), ESTX 50 PR.EUR (STOXX50E), KOSPI Composite (KS11), IBEX 35 (IBEX), Nikkei 225 (N225), AEX (AEX), DAX PERFORMANCE (GDAXI), IBOVESPA (BVSP), S&P/TSX Composite (GSPTSE), IPC MEXICO (MXX), SMI PR (SSMI), Dow Jones Industrial Average (DJI), HANG SENG INDEX (HSI), TSEC weighted index (TWII), NASDAQ Composite (IXIC), BEL 20 (BFX), Austrian Traded Index in EUR (ATX), Jakarta Composite Index (JKSE). The details of these datasets are listed in Table 1 and Table 2, respectively.

In this paper, support vector regression and twin support vector regression formulations are discussed in detail and applied to an individual companies’ stock indices in the area of information technology industries, banking, oil, and petroleum industry and stock market index datasets of different countries to predict stock prices. Here, a pair of smaller sized QPPs is solved instead of a single large sized QPP, as in the case of SVR, thus yielding a reduction in the cost of the system. To verify the effectiveness of TSVR, we performed numerical experiments for both linear and Gaussian kernels on financial time series datasets. In experimental results, TSVR shows better learning speed for both linear and Gaussian kernels with the ability to predict having a better generalization ability than SVR. In fact, the computation time of the TSVR is approximately four times lower than the standard SVR in terms of learning speed, which clearly indicates its existence and usability. In future work, a new model that is able to handle noise and outliers for predicting the prices of stock indices can be explored.

 

Source:

http://doi.org/10.1371/journal.pone.0211402

 

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